Simplify. Remove all perfect squares from inside the square root. V75 =​

Answer:

Part A)

2nd and 5th choice.

Part B)

[tex]\displaystyle y=-\frac{1}{4}x^2-\frac{3}{2}x+\frac{3}{4}[/tex]

Step-by-step explanation:

For the given parabola, our focus is (-3, 2), and our directrix is given by y = 4.

Part A)

We are given a point (x, y) on the parabola.

Since our directrix is an equation of y, the distance from (x, y) to the directrix will simply be the absolute value of the difference in y-values. So:

[tex]d_1=|y-4|=|4-y|[/tex]

Recall the distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

Our distance from (x, y) to the focus (-3, 2) can be determined using the distance formula. Let (x, y) be (x₂, y₂) and let our focus (-3, 2) be (x₁, y₁). Therefore:

[tex]d_2=\sqrt{(x-(-3))^2+(y-2)^2}=\sqrt{(x+3)^2+(y-2)^2[/tex]

Hence, for Part A, our answers are the 2nd and 5th choices.

Part B)

Recall that by the definition of a parabola, any point (x, y) on it is equidistant to the directrix and focus. Hence:

[tex]\sqrt{(x+3)^2+(y-2)^2}=|y-4|[/tex]

Solve for y. Square both sides. We may remove the absolute value since anything squared is positive:

[tex](x+3)^2+(y-2)^2=(y-4)^2[/tex]

Square:

[tex]x^2+6x+9+y^2-4y+4=y^2-8y+16[/tex]

Rearrange:

[tex](x^2+6x+13)+(-16)=(y^2-y^2)+(-8y+4y)[/tex]

Combine like terms:

[tex]x^2+6x-3=-4y[/tex]

Divide both sides by -4. Hence, our equation is:

[tex]\displaystyle y=-\frac{1}{4}x^2-\frac{3}{2}x+\frac{3}{4}[/tex]

Heyo! :D

Distance to the directrix is |y - 4|.

Distance to the focus is [tex]\sqrt{(x+3)^2+(y-2)^2}[/tex].

Hope this helps! If so, please lmk! Tysm and good luck!

Answer:

let number be n

by question

(5n+3)=(n-9)

5n-n=-9-3

4n=-12

n=-12/4=-3

required no. is -3.

Denote x2 by y.

(x2-3)7=(y-3)7

This is a binomial expansion in y, and you want the coefficient of y4 because y4=x8

You have 7 terms of (y-3) in (y-3)7.  To get the fourth power of y, you need to choose y from four of the terms.  The number of ways you can do this is the combinations of 7 things taken 4 at a time.  This is:

7!/(4!3!)=35

So, the coefficient of x8 in the given expansion will be 210.

HOPE IT HELPS

THANK YOU

Answer:

Some Facts about lines (1) For non vertical line L, if L passes a point (x0,y0) with slope m, then an equation of line L is y − y0 = m(x − x0). (2) If a non vertical line L passes through distinct points (x1,y1) and x2(y2), then the slope of L is m = y2 − y1 x2 − x1 . x a + y b = 1.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

21 is the answer your welcome

Answer:

37

Step-by-step explanation:

Answer:

Step-by-step explanation:

C is 135'

A is 90'

B is 90'

D is 45'

E is 45'

F is 135'

Answer:

I'ma just take the free points, Give the other person a brainlest

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Because the term behind the 7 is a x, but the 3 only has a plus sign. If both numbers had a x, then yes

Hope this Helps!!!

Answer:

The 1st, 4th, and 5th triangles are right triangles

Step-by-step explanation:

Right triangles always have a key characteristic. They all have an angle of 90 degrees. Keep an eye out for that.

Answer:

B.

Step-by-step explanation:

Answer:

26

Show Your Work:

Answer:

26 sq.ft.

Step-by-step explanation:

i did the diagnostic

Answer:

Car B is travelling at the faster speed.

Step-by-step explanation:

Given that,

The distance covered by car A = 100 m

Time of car A, t = 5 s

The distance covered by car B = 100 m

Time of car B, t = 2 s

We need to find which one is travelling at the faster speed.

Speed = distance/time

For car A,

[tex]v_A=\dfrac{100\ m}{5\ s}\\\\v_A=20\ m/s[/tex]

For car B,

[tex]v_B=\dfrac{100\ m}{2\ s}\\\\v_B=50\ m/s[/tex]

So, car B is travelling at the faster speed.

Answer:

76%

Step-by-step explanation:

76% is 0.76

So it's is greater than 0.67

76%>0.67

Answer (this one's written in slope-intercept form):

[tex]y= \frac{3}{5}x -3[/tex]

Step-by-step explanation:

1) Lines that are parallel to each other have the same slope. The line [tex]y=\frac{3}{5} x-8[/tex] is in slope intercept form, or [tex]y = mx + b[/tex] form, and the number in place of [tex]m[/tex] represents the slope. Knowing this, it looks like [tex]\frac{3}{5}[/tex] is in the place of the [tex]m[/tex] in that equation, so  [tex]\frac{3}{5}[/tex] is the slope - and the slope we need to use for the answer, too.

2) Once you know a point that the line must pass through and a slope, you can write an equation with point-slope form, or [tex]y-y_1 = m (x - x_1)[/tex]. [tex]m[/tex] is the slope and [tex]x_1[/tex] and [tex]y_1[/tex] are the x and y values of the point it must pass through. So, substitute [tex]\frac{3}{5}[/tex] for [tex]m[/tex], 0 for [tex]x_1[/tex], and -3 for [tex]y_1[/tex]. Simplify and isolate y to put it in slope-intercept form:

[tex]y-(-3) = \frac{3}{5} (x - 0) \\y + 3 = \frac{3}{5} x - 0 \\y = \frac{3}{5} x - 3[/tex]

3) Thus, [tex]y = \frac{3}{5} x - 3\\[/tex] is the answer. It's written in slope-intercept form.

Answer:

73.2 cm³

Step-by-step explanation:

The volume of the cylinder without the prism is V" = volume of cylinder, V' - volume of rectangular prism, V

Volume of cylinder = πr²h where r = radius of cylinder = 2 cm and h = height of cylinder = 6 cm.

So, V = πr²h

= π(2 cm)²(6 cm)

= π × 4 cm² × 6 cm

= 24π cm³

= 75.4 cm³

V = volume of rectangular prism = Area of 0.6 cm square × height = L²h where L = 0.6 cm and h = height of rectangular prism = 6 cm.

So, V = L²h = (0.6 cm)² × 6 cm = 2.16 cm³

volume of the cylinder without the prism is V" = V' - V

= 75.4 cm³ - 2.16 cm³

= 73.24 cm³

≅  73.2 cm³

Answer:

Not an answer

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

9514 1404 393

Answer:

  250,000

Step-by-step explanation:

The thousands digit is more than 4, so the ten-thousands digit is increased by 1 before digits to its right are replaced by zeros. The rounded number is ...

  250,000

Answer:

Under couch

Step-by-step explanation:

We can find the slope by using the slope formula. Also know rise over run.

[tex] \large \bold{m = \frac{rise}{run} }[/tex]

[tex]m = \frac{2 - 0}{ - 2 - 2} \\ m = \frac{2}{ - 4} \\ m = - \frac{1}{2} [/tex]

From the slope-intercept y = mx+b.

[tex] \large \bold {m = slope } \\ \large \bold {b = y - intercept }[/tex]

[tex] \large \boxed { - \frac{1}{2} }[/tex]

Answer:

-1/2

Step-by-step explanation:

Going from (-2, 2) to (2, 0), x (the run) increases by 4 and y (the rise) decreases by 2.  Thus, the slope of this line is m = rise / run = -2/4 = -1/2.

i think its C because don't you have to add the numbers together

The answer is 40 degrees :]

Answer:

434.9 cm³

Step-by-step explanation:

Volume of a sphere: 4/3πr³

Substitute the information to find the volume.

4/3π(4.7)³ = 434.9

Answer:

The distance from the boat to the foot of the lighthouse is 359.36 ft

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, From the top of a lighthouse 160 feet high, the angle of depression of a boat out at sea is 24.

The whole situation is representing a right triangle (refer to figure)

Let  the distance from the boat to the foot of the lighthouse be x

We know that, angle of depression = angle of elevation

Then, using formula of height and distance,

tan 24° = 160 / x

x = 160 / tan 24°

x = 359.36

Hence,  the distance from the boat to the foot of the lighthouse is 359.36 ft

For more references on height and distance, click;

https://brainly.com/question/15939509

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Answer:

5

Step-by-step explanation:

33p is separated into 3p and 2p

4 more 2p than 3p

5 3 points

9 2 points